arXiv subjects

K. Sznajd-Weron

Publications and source records attributed to K. Sznajd-Weron.

5 recordsLinked to original sources

arXiv2011

Phase transition in the Sznajd model with independence

We propose a model of opinion dynamics which describes two major types of social influence -- conformity and independence. Conformity in our model is described by the so called outflow dynamics (known as Sznajd model). According to sociologists' suggestions, we introduce also a second type of social influence, known in social psychology as independence. Various social experiments have shown that the level of conformity depends on the society. We introduce this level as a parameter of the model and show that there is a continuous phase transition between conformity and independence.

physics.soc-ph↗

arXiv2007

Some new results on one-dimensional outflow dynamics

In this paper we introduce modified version of one-dimensional outflow dynamics (known as a Sznajd model) which simplifies the analytical treatment. We show that simulations results of the original and modified rules are exactly the same for various initial conditions. We obtain the analytical formula for exit probability using Kirkwood approximation and we show that it agrees perfectly with computer simulations in case of random initial conditions. Moreover, we compare our results with earlier analytical calculations obtained from renormalization group and from general sequential probabilistic frame introduced by Galam. Using computer simulations we investigate the time evolution of several correlation functions to show if Kirkwood approximation can be justified. Surprisingly, it occurs that Kirkwood approximation gives correct results even for these initial conditions for which it cannot be easily justified.

cond-mat.stat-mech↗

arXiv2002

How effective is advertising in duopoly markets?

A simple Ising spin model which can describe the mechanism of advertising in a duopoly market is proposed. In contrast to other agent-based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spread of opinions among customers. It is shown via standard Monte Carlo simulations that very simple rules and inclusion of an external field -- an advertising campaign -- lead to phase transitions.

cond-mat.stat-mech↗

arXiv2002

Hierarchical population model with a carrying capacity distribution

A time- and space-discrete model for the growth of a rapidly saturating local biological population $N(x,t)$ is derived from a hierarchical random deposition process previously studied in statistical physics. Two biologically relevant parameters, the probabilities of birth, $B$, and of death, $D$, determine the carrying capacity $K$. Due to the randomness the population depends strongly on position, $x$, and there is a distribution of carrying capacities, $Π(K)$. This distribution has self-similar character owing to the imposed hierarchy. The most probable carrying capacity and its probability are studied as a function of $B$ and $D$. The effective growth rate decreases with time, roughly as in a Verhulst process. The model is possibly applicable, for example, to bacteria forming a "towering pillar" biofilm. The bacteria divide on randomly distributed nutrient-rich regions and are exposed to random local bactericidal agent (antibiotic spray). A gradual overall temperature change away from optimal growth conditions, for instance, reduces bacterial reproduction, while biofilm development degrades antimicrobial susceptibility, causing stagnation into a stationary state.

physics.bio-ph↗

arXiv2001

A simple model of price formation

A simple Ising spin model which can describe the mechanism of price formation in financial markets is proposed. In contrast to other agent-based models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spread of opinions among traders. It is shown via standard Monte Carlo simulations that very simple rules lead to dynamics that duplicate those of asset prices.

cond-mat.stat-mech↗